推广闭参数曲面形态分解的球谐函数
Spheroidal harmonics for generalizing the morphological decomposition of closed parametric surfaces
AI总结：
本文提出球体谐函数（SOH）方法，通过引入可调参数最小化几何畸变，克服了球谐函数在分析扁球和长球颗粒时的振荡缺陷，提升了颗粒形态分析质量。
摘要：
球谐函数（SH）已被广泛用作分析颗粒力学中颗粒形态的基础。SH的使用通过将颗粒坐标映射到单位球面上来实现，在实践中通常是对径向坐标的直接缩放。然而，当应用于扁球或长球形状的颗粒时，SH分析质量会退化，重建后会出现显著的振荡。在此，我们提出了一种球体谐函数（SOH）方法，用于长球和扁球颗粒的展开与重建。该方法通过提供可针对每个颗粒调整以最小化几何畸变的额外参数来推广SH方法，从而提高分析质量。我们提出了三种映射技术，用于将星形和非星形颗粒处理到球体域上。结果表明，SOH能够克服SH的缺点，且无需计算昂贵的解决方案或对现有代码和处理流程进行大幅更改。
英文摘要：
Spherical harmonics (SH) have been extensively used as a basis for analyzing the morphology of particles in granular mechanics. The use of SH is facilitated by mapping the particle coordinates onto a unit sphere, in practice often a straightforward rescaling of the radial coordinate. However, when applied to oblate- or prolate-shaped particles the SH analysis quality degenerates with significant oscillations appearing after the reconstruction. Here, we propose a spheroidal harmonics (SOH) approach for the expansion and reconstruction of prolate and oblate particles. This generalizes the SH approach by providing additional parameters that can be adjusted per particle to minimize geometric distortion, thus increasing the analysis quality. We propose three mapping techniques for handling both star-shaped and non-star-shaped particles onto spheroidal domains. The results demonstrate the ability of the SOH to overcome the shortcomings of SH without requiring computationally expensive solutions or drastic changes to existing codes and processing pipelines.
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